Offsets, rolling offsets and bend arcs from centreline geometry
Three layout jobs, all computed from the same centreline trigonometry an electrician’s multiplier table abbreviates. Offset: from the offset height and bend angle, the distance between bend centres, the travel (run) length, and the shrink the conduit pulls back, which is the figure conduit lengths are laid out by. Rolling offset: rise and set combine into the true offset by Pythagoras before the same angle geometry applies. Bend arc: from a centreline radius and angle, the developed arc length (the conduit actually consumed by the bend), the tangent length and the setback. The convention is stated once and held throughout: all marks and lengths are centreline geometry; your bender’s own take-up and gain allowances, which vary by tool, are applied from its chart as the content explains.
Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice. Bender-specific allowances come from the tool manufacturer’s data; verify layouts against the work and the governing electrical or piping code.
What this calculator does
An offset is a right triangle wearing work clothes: the offset height is the side opposite the bend angle, the distance between the two bend centres is the hypotenuse (height / sin of the angle), and the travel along the run is the adjacent side (height / tan). Shrink, the length the finished run loses versus its straight-line layout, is simply hypotenuse minus travel, here computed exactly instead of read from a per-angle constant table. The rolling offset first collapses two perpendicular shifts into the one true offset the triangle needs, rise and set combining by Pythagoras, a step field layouts botch when they treat one direction and hope. The arc tool prices a single bend honestly: developed length along the centreline, tangent length to the bend’s start, and the setback a fitting or stub layout consumes.
How to use it
- Marks are centreline marks. Hand benders mark and bend to their own reference points (arrow, star, rim notch) with take-up allowances from the tool’s chart: transfer the centre distances computed here onto the conduit using your bender’s documented method rather than treating these figures as shoe positions.
- Angle choice is a space and shrink bargain. Shallow angles (10 and 22.5 degrees) spread bends far apart with little shrink and gentle pulling; 45 and 60 pack tightly but shrink grows and wire pulls harder. The table in the results reading repays a glance before committing.
- Rolling offsets must be measured in both planes. Rise alone under-measures the true offset and the fitting arrives angled; measure the set with the same care as the rise.
- Radius belongs to the bender and size. Centreline radius differs by tool and conduit diameter; the value printed on the bender or in its manual is the input the arc figures deserve.
The formulas
- Offset: distance between bend centres = height / sin(angle); travel = height / tan(angle); shrink = distance – travel.
- Rolling offset: true offset = √(rise² + set²), then the offset formulas with the same angle.
- Single bend: developed arc = angle in radians × centreline radius; tangent length = radius × tan(angle / 2); setback for a stub = tangent length.
Worked examples
The 30-degree offset. A 200 mm offset at 30 degrees: the bend centres sit 400.00 apart, the travel along the run is 346.41, and the shrink is 53.59: lay the run out 53.59 shorter than the naive sum of its straight pieces, or the far end arrives long by exactly that. At 45 degrees the same offset packs into 282.84 between centres with a shrink of 82.84, the trade the angle choice prices.
The rolling offset. Rise 150 and set 200: the true offset is √(150² + 200²) = 250.00, and at 45 degrees the travel between bend centres is 353.55. A layout that used either 150 or 200 as “the offset” would miss in two directions at once, which is the entire reason this mode exists.
The 90-degree bend. On a 150 centreline radius, the bend consumes 235.62 of conduit along its arc, and the tangent (the setback from the corner to where the bend starts) is the full 150.00: a stub-up’s mark is its target height minus that setback, then refined by the bender’s own take-up figure.
Reading your results
Read shrink as length already spent: conduit cut lists that ignore it produce runs that grow, and the growth compounds across multiple offsets on one stick. Read the between-centres distance as the number that must fit the physical space, ceiling voids and box spacings included. And read the multipliers this geometry implies (2.00 at 30 degrees, 1.41 at 45, 3.86 at 15, 5.76 at 10) as the field table they are: the calculator and the laminated card agree because both are the same triangle.
Limitations
- Bender allowances are tool-specific. Take-up, gain and springback compensation vary by manufacturer, conduit type and wall; the brief for this page requires those to come from documented tool data, so they are deliberately not tabulated here.
- Springback is real. Conduit and pipe relax a degree or two after bending; overbend-by-experience is a craft correction no geometry page can make for your material batch.
- Saddles and multi-bend layouts compose these primitives. Three and four-point saddles are offsets with a centre bend; their mark spacings follow from the same triangles plus the bender’s shrink constants, and are laid out from the offset results rather than a separate black box.
- Centreline convention throughout. Inside and outside dimensions of the finished bend differ by the conduit’s radius on each side; fittings dimensioned to faces need that adjustment added locally.
Frequently asked questions
What exactly is shrink, and why does conduit “lose” length?
Nothing is lost; the diagonal is longer than the run it replaces. An offset’s two bends exchange a straight segment (the travel) for a diagonal path (the between-centres distance), and the diagonal is longer by the shrink amount, so a conduit cut to the sum of the straight measurements arrives short at the far end unless layout adds the diagonal’s extra length back, which is what marking by shrink accomplishes. The steeper the angle, the longer the diagonal relative to its run, and the bigger the correction: 53.59 on the 30-degree example, 82.84 at 45.
Why do the multiplier tables and this calculator agree?
Because the tables are this trigonometry pre-computed: the multiplier is 1 / sin(angle), the shrink constant is the multiplier minus 1 / tan(angle), expressed per unit of offset. Tables round to workshop-friendly fractions (a shrink of about 3/8 inch per inch of offset at 45 degrees, in the common imperial card) while the calculator keeps full precision; on long offsets the accumulated rounding is exactly why computed layouts beat card layouts.
How do I lay out a three-point saddle from these tools?
A saddle is an offset wrapped around an obstruction: the centre bend (usually 45 degrees) crosses the obstacle and two outer bends (usually 22.5) restore the run. Use the offset mode with the obstruction’s height as the offset height for the centre geometry, space the outer marks by the same between-centres logic at their angle, and apply your bender’s saddle shrink constant from its chart, since saddle marking conventions (centre-of-bend versus centre-of-obstruction references) are where tool documentation, not geometry, governs.
Does the conduit size change the offset maths?
The centreline triangle does not care about diameter: a 200 mm offset is a 200 mm offset in any size. Size enters through the bender (its radius, take-up and the minimum spacing the shoe needs) and through springback behaviour, which is why the calculator separates the geometry it can state exactly from the allowances it insists you take from the tool’s own data.
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Method: centreline right-triangle geometry for offsets (Pythagorean combination for rolling offsets) and circular arc relations for single bends; bender allowances referred to manufacturer data. Last reviewed: 14 October 2026.